LYZ ellipsoid and Petty projection body for log-concave functions

Some remarks on Petty projection of log-concave functions

“…

In this note we study the Petty projection of a log-concave function, which has been recently introduced in [9]. Moreover, we present some new inequalities involving this new notion, partly complementing and correcting some results from [9].

…”

$L_p$ John ellipsoids for log-concave functions

“…Also an extension of the John ellipsoids to the case of log-concave functions has attracted a lot of authors interest, for example, in [5], the authors extend the notion of John's ellipsoid to the setting of integrable log-concave functions and obtain integral ratio of a log-concave function and establish the reverse functional affine isoperimetric inequality. The extension of the LYZ ellipsoid to the log-concave functions is done by Fang and Zhou [27]. The Löwner ellipsoid function for log-concave function is invested by Li, Schütt and Werner [40].…”

Dual curvature measures on convex functions and associated Minkowski problems

“…Actually an analytic inequality contains more information than its corresponding geometric inequality. During the past decades, many analytic inequalities with geometric background were found [1][2][3][4]10,15,16,[22][23][24]26,27,42,54,59] basically from the viewpoint of integral and convex geometry.…”